Distributed hash table

Most DHTs use some variant of consistent hashing or rendezvous hashing to map keys to nodes. The two algorithms appear to have been devised independently and simultaneously to solve the distributed hash table problem.

Both consistent hashing and rendezvous hashing have the essential property that removal or addition of one node changes only the set of keys owned by the nodes with adjacent IDs, and leaves all other nodes unaffected. Contrast this with a traditional hash table in which addition or removal of one bucket causes nearly the entire keyspace to be remapped. Since any change in ownership typically corresponds to bandwidth-intensive movement of objects stored in the DHT from one node to another, minimizing such reorganization is required to efficiently support high rates of churn (node arrival and failure).

Consistent hashing employs a function ${\displaystyle \delta (k_{1},k_{2})}$ that defines an abstract notion of the distance between the keys ${\displaystyle k_{1}}$ and ${\displaystyle k_{2}}$, which is unrelated to geographical distance or network latency. Each node is assigned a single key called its identifier (ID). A node with ID ${\displaystyle i_{x}}$ owns all the keys ${\displaystyle k_{m}}$ for which ${\displaystyle i_{x}}$ is the closest ID, measured according to ${\displaystyle \delta (k_{m},i_{x})}$.

For example, the Chord DHT uses consistent hashing, which treats nodes as points on a circle, and ${\displaystyle \delta (k_{1},k_{2})}$ is the distance traveling clockwise around the circle from ${\displaystyle k_{1}}$ to ${\displaystyle k_{2}}$. Thus, the circular keyspace is split into contiguous segments whose endpoints are the node identifiers. If ${\displaystyle i_{1}}$ and ${\displaystyle i_{2}}$ are two adjacent IDs, with a shorter clockwise distance from ${\displaystyle i_{1}}$ to ${\displaystyle i_{2}}$, then the node with ID ${\displaystyle i_{2}}$ owns all the keys that fall between ${\displaystyle i_{1}}$ and ${\displaystyle i_{2}}$.

In rendezvous hashing, also called highest random weight (HRW) hashing, all clients use the same hash function ${\displaystyle h()}$ (chosen ahead of time) to associate a key to one of the n available servers. Each client has the same list of identifiers {S₁, S₂, ..., S_n }, one for each server. Given some key k, a client computes n hash weights w₁ = h(S₁, k), w₂ = h(S₂, k), ..., w_n = h(S_n, k). The client associates that key with the server corresponding to the highest hash weight for that key. A server with ID ${\displaystyle S_{x}}$ owns all the keys ${\displaystyle k_{m}}$ for which the hash weight ${\displaystyle h(S_{x},k_{m})}$ is higher than the hash weight of any other node for that key.

Locality-preserving hashing ensures that similar keys are assigned to similar objects. This can enable a more efficient execution of range queries, however, in contrast to using consistent hashing, there is no more assurance that the keys (and thus the load) is uniformly randomly distributed over the key space and the participating peers. DHT protocols such as Self-Chord and Oscar[14] address such issues. Self-Chord decouples object keys from peer IDs and sorts keys along the ring with a statistical approach based on the swarm intelligence paradigm.[15] Sorting ensures that similar keys are stored by neighbour nodes and that discovery procedures, including range queries, can be performed in logarithmic time. Oscar constructs a navigable small-world network based on random walk sampling also assuring logarithmic search time.

Each node maintains a set of links to other nodes (its neighbors or routing table). Together, these links form the overlay network.[16] A node picks its neighbors according to a certain structure, called the network's topology.

All DHT topologies share some variant of the most essential property: for any key k, each node either has a node ID that owns k or has a link to a node whose node ID is closer to k, in terms of the keyspace distance defined above. It is then easy to route a message to the owner of any key k using the following greedy algorithm (that is not necessarily globally optimal): at each step, forward the message to the neighbor whose ID is closest to k. When there is no such neighbor, then we must have arrived at the closest node, which is the owner of k as defined above. This style of routing is sometimes called key-based routing.

Beyond basic routing correctness, two important constraints on the topology are to guarantee that the maximum number of hops in any route (route length) is low, so that requests complete quickly; and that the maximum number of neighbors of any node (maximum node degree) is low, so that maintenance overhead is not excessive. Of course, having shorter routes requires higher maximum degree. Some common choices for maximum degree and route length are as follows, where n is the number of nodes in the DHT, using Big O notation:

Max. degree	Max route length	Used in	Note
${\displaystyle O(1)}$	${\displaystyle O(n)}$		Worst lookup lengths, with likely much slower lookups times
${\displaystyle O(1)}$	${\displaystyle O(\log n)}$	Koorde (with constant degree)	More complex to implement, but acceptable lookup time can be found with a fixed number of connections
${\displaystyle O(\log n)}$	${\displaystyle O(\log n)}$	Chord Kademlia Pastry Tapestry	Most common, but not optimal (degree/route length). Chord is the most basic version, with Kademlia seeming the most popular optimized variant (should have improved average lookup)
${\displaystyle O(\log n)}$	${\displaystyle O(\log n/\log(\log n))}$	Koorde (with optimal lookup)	More complex to implement, but lookups might be faster (have a lower worst case bound)
${\displaystyle O({\sqrt {n}})}$	${\displaystyle O(1)}$		Worst local storage needs, with much communication after any node connects or disconnects

The most common choice, ${\displaystyle O(\log n)}$ degree/route length, is not optimal in terms of degree/route length tradeoff, but such topologies typically allow more flexibility in choice of neighbors. Many DHTs use that flexibility to pick neighbors that are close in terms of latency in the physical underlying network. In general, all DHTs construct navigable small-world network topologies, which trade-off route length vs. network degree.[17]

Maximum route length is closely related to diameter: the maximum number of hops in any shortest path between nodes. Clearly, the network's worst case route length is at least as large as its diameter, so DHTs are limited by the degree/diameter tradeoff[18] that is fundamental in graph theory. Route length can be greater than diameter, since the greedy routing algorithm may not find shortest paths.[19]

Aside from routing, there exist many algorithms that exploit the structure of the overlay network for sending a message to all nodes, or a subset of nodes, in a DHT.[20] These algorithms are used by applications to do overlay multicast, range queries, or to collect statistics. Two systems that are based on this approach are Structella,[21] which implements flooding and random walks on a Pastry overlay, and DQ-DHT, which implements a dynamic querying search algorithm over a Chord network.[22]

• Apache Cassandra
• BATON Overlay
• Mainline DHT – standard DHT used by BitTorrent (based on Kademlia as provided by Khashmir)[30]
• Content addressable network (CAN)
• Chord
• Koorde
• Kademlia
• Pastry
• P-Grid
• Riak
• Tapestry
• TomP2P
• Voldemort

• BTDigg: BitTorrent DHT search engine
• Codeen: web caching
• Freenet: a censorship-resistant anonymous network
• GlusterFS: a distributed file system used for storage virtualization
• GNUnet: Freenet-like distribution network including a DHT implementation
• I2P: An open-source anonymous peer-to-peer network
• I2P-Bote: serverless secure anonymous email
• IPFS: A content-addressable, peer-to-peer hypermedia distribution protocol
• JXTA: open-source P2P platform
• LBRY: A blockchain-based content sharing protocol which uses a Kademlia-influenced DHT system for content distribution
• Oracle Coherence: an in-memory data grid built on top of a Java DHT implementation
• Perfect Dark: a peer-to-peer file-sharing application from Japan
• Retroshare: a Friend-to-friend network[31]
• Jami: a privacy-preserving voice, video and chat communication platform, based on a Kademlia-like DHT
• Tox: an instant messaging system intended to function as a Skype replacement
• Twister: a microblogging peer-to-peer platform
• YaCy: a distributed search engine